The subject matter of this specification relates to a new Adjoint Method (and associated System and Program Storage Device) for Calculating Gradients, and, in particular, to an Adjoint Method for Calculating Gradients of an objective function with respect to changes in valve settings, while taking into account the modeling of pressure drop and fluid flow along a wellbore, for more effectively and efficiently optimizing settings of control valves for reservoir production.
Controllable down-hole devices have made feasible the implementation of advanced well control strategies for achieving an objective, such as maximizing hydrocarbon recovery or net present value. However, the development of algorithms for determining the best strategy for controlling these devices, subject to production and injection constraints, is still an area of active research, and generally involves implementation of some form of control logic within a reservoir simulation workflow.
Some ‘control strategies’ for controlling these devices are reactive, meaning that interventions are made when local conditions are met at particular wells or valves, without taking into account the future effect of the intervention on the entire reservoir. Moreover, with this approach, it may already be too late to intervene to prevent unwanted breakthrough. These production rule methods tend to be heuristic, but are very efficient in reservoir simulation. Alternative proactive control strategies apply to the lifetime of the field, and thus provide a mechanism to control fluid flow early enough to delay breakthrough. These ‘alternative proactive control strategies’ for controlling these devices can be divided into at least two methods: (1) ‘stochastic’ methods, such as Monte Carlo which investigate the effect of a large number of possible strategies, and (2) ‘deterministic’ methods which set the behavior of each well and valve based on its effect on the objective. This specification includes a ‘proactive deterministic constrained optimization method’ associated with the aforementioned ‘alternative proactive control strategies’ adapted for controlling the aforementioned ‘controllable downhole devices’. In particular, this specification includes a first application of adjoint gradients to control and optimize settings in a multi-segmented well model.